You are given the following equation
DOG + DOG + DOG + DOG + DOG + DOG = BRO, where each letter stands for a digit.
What is the value of DOG?
Step by Step Explanation:
- We know the following from the question
- Both DOG and BRO are 3 digit numbers.
- The middle digit of the first one is the last digit of the 2nd one. The other digits are different from each other.
- Also, 6 × DOG = BRO
- Now we need to apply logic to see if we can solve it. Let's see what we can figure out.
- Hmm...'D' cannot be more than 1, because if it was then 6 × DOG would be a 4 digit number i.e. even the smallest value of DOG in that case would be 200, and 200 × 6 = 1200, which is a 4 digit number.
So, D = 1
- For the same reason O cannot be more than 6. (As, 170 × 6 = 1020 is a 4 digit number)
- Now think about G. Can it be even?
No - it cannot be. Why?
6 multiplied by any even number results in the same last digit (6 × 2 = 12, 6 × 4 = 24, 6 × 6 = 36 and so on). But we know that the last digits of DOG and BRO are different.
So G is odd. It can't be 1 though, because D=1. (The value of S and X cannot be same.)
So G either is 3,5,7 or 9.
It cannot be 3, because 3 × 6 = 18. This means O is 8, and we already know O is not greater than 6.
Now it's just a matter of elimination.
- The possibilities are
G = 5 and O = 0
G = 7 and O = 2
G = 9 and O = 4
- Now you have 3 possibilities for DOG (105, 127 and 149). It is easy enough to multiply them by 6 and see which one results in the right possibility.
- 105 × 6 = 630
127 × 6 = 762
149 × 6 = 894
- 127 × 6 = 762 is not correct, since last digit of DOG should not be same as first digit of BRO.
- 149 × 6 = 894 is also not correct, since last digit of DOG should not be same as middle digit of BRO.
- Therefore, correct value of DOG is 105.
You can reuse this answer
Creative Commons License